Artikel ini memberikan latihan soal beserta pembahasan Penilaian Tengah Semester 2019 matematika IPS kelas 12
—
Apa sih mata pelajaran yang menurut kamu paling sulit? Pasti salah satunya adalah matematika ‘kan? Untuk menguasai seluruh materi matematika di Penilaian Tengah Semester, kamu tentu membutuhkan banyak latihan. Nah tunggu apalagi, ayo langsung saja simak latihan soal beserta pembahasan Penilaian Tengah Semester matematika IPS kelas 12 berikut ini.
Topik: Bidang Datar
Subtopik: Prinsip Kesebangunan
- Perhatikan gambar bangun datar di bawah ini!
Jika garis DE sejajar garis FG sejajar garis BC maka nilai
Jawaban: C
Pembahasan:
Perhatikan segitiga ADE sebangun dengan segitiga AFG sehingga diperoleh persamaan:
Kemudian perhatikan segitiga ADE sebangun dengan segitiga ABC sehingga diperoleh persamaan :
Jadi nilai
Topik: Bidang Datar
Subtopik: Dalil Dua Garis
2. Perhatikan gambar di bawah ini!
Jika garis DE sejajar dengan garis BC dan panjang AD = 4 cm, BD = 6 cm, AE = x cm dan EC = 9 cm maka nilai dari
- 8
- 9
- 10
- 12
- 18
Jawaban: D
Pembahasan:
Gunakan dalil intersep untuk gambar pada soal.
Maka nilai dari
Topik: Bidang Datar
Subtopik: Dalil Menelaus & Dalil Ceva
3. Perhatikan gambar di bawah ini!
Nilai yang tepat untuk gambar di atas adalah ….
- 2,5
- 3,0
- 3,5
- 4,0
- 4,5
Jawaban: D
Pembahasan:
Gunakan dalil Menelaus untuk gambar pada soal.
Topik: Bidang Datar
Subtopik: Garis Istimewa Segitiga I
4. Perhatikan gambar berikut ini!
Jika luas segitiga ACD dan BCD berturut-turut adalah dan maka panjang BD adalah ….
- 4,0
- 4,5
- 5,0
- 5,5
- 6,0
Jawaban: D
Pembahasan:
Perhatikan bahwa:
Topik: Bidang Ruang: Kedudukan dan Proyeksi
Subtopik: Ulasan Bangun Ruang
5. Perhatikan bangun ruang di bawah ini.
Bangun ruang yang tidak memiliki diagonal ruang adalah ….
- (i) dan (ii)
- (ii) dan (iii)
- (i) dan (iii)
- (ii) dan (iv)
- (i) dan (iv)
Jawaban: E
Pembahasan:
Ingat bahwa diagonal ruang adalah ruas garis yang menghubungkan dua titik sudut yang berhadapan dalam suatu bangun ruang.
Pada gambar (i) dan (iv) hanya terdapat diagonal sisi saja (garis biru).
Topik: Bidang Ruang: Kedudukan dan Proyeksi
Subtopik: Kedudukan Garis terhadap Garis
6. Garis yang sejajar dengan garis AH adalah….
- CF
- EF
- EC
- DC
- CH
Jawaban: A
Pembahasan:
Garis AH berada pada bidang ADHE, sedangkan bidang yang sejajar dengan ADHE adalah bidang BCGF, maka garis yang sejajar dengan bidang AH adalah garis yang berada pada bidang BCGF. Jadi garis AH sejajar dengan CF.
Garis AH bersilangan dengan garis EF, EC dan DC.
Garis AH berpotongan dengan CH di titik H.
Topik: Bidang Ruang: Kedudukan dan Proyeksi
Subtopik: Kedudukan Bidang terhadap Bidang
7. Perhatikan kubus di bawah ini.
Bidang AFH dan bidang BDG adalah bidang yang saling ….
- Sejajar karena memiliki satu garis persekutuan
- Sejajar karena tidak memiliki garis persekutuan
- Berpotongan karena memiliki titik potong
- Berpotongan karena memiliki garis potong
- Bersilangan karena tidak saling bertemu
Jawaban: B
Pembahasan:
Perhatikan gambar kedua bidang tersebut.
Dari gambar di atas maka kedua bidang saling sejajar karena tidak memiliki garis persekutuan.
Topik: Bidang Ruang: Jarak
Subtopik: Jarak Titik ke Titik
8. Diketahui sebuah kubus ABCD.EFGH dengan rusuk 8 cm seperti pada gambar di bawah ini.
Jika titik P terletak pada garis AG dengan AP : AG = 1 : 4, maka jarak titik B ke titik P adalah ….
Jawaban: A
Pembahasan:
Perhatikan gambar kubus di bawah ini.
Diketahui rusuk = 8 cm maka,
Dari segitiga siku-siku ABG diperoleh :
Sedangkan dengan menggunakan aturan cos pada segitiga APB maka diperoleh :
Jadi jarak titik B ke titik P adalah
Topik: Bidang Ruang: Jarak
Subtopik: Jarak Titik ke Garis
9. Diketahui kubus ABCD.EFGH dengan rusuk 5 cm seperti gambar di bawah ini. Jarak titik E ke rusuk BC adalah ….
Jawaban: A
Pembahasan:
Perhatikan segitiga EBC pada kubus di bawah ini.
Karena segitiga EBC adalah segitiga siku-siku di B maka jarak terdekat titik E ke garis BC adalah EB
Topik: Bidang Ruang: Jarak
Subtopik: Jarak Dua Garis Bersilangan
10. Diketahui limas T.ABCD dengan alas berbentuk persegi. Rusuk tegak 10 cm dan rusuk alas 8 cm. Jika titik M adalah titik tengah rusuk AD maka jarak garis TM ke garis AB adalah …. Cm
- 2
- 3
- 4
- 5
- 6
Jawaban: C
Pembahasan:
Perhatikan gambar di bawah ini.
Jika kita buat bidang yang sejajar garis AB dan memuat garis TM yaitu bidang TMN seperti gambar di bawah ini maka jarak
Maka jaraknya berubah jadi jarak garis sejajar bidang.
Misalkan titik P dan Q berturut-turut adalah titik tengah rusuk AB dan garis MN, kemudian proyeksikan titik P ke garis TQ seperti pada gambar di bawah ini.
Karena TPQ adalah segitiga siku-siku di Q maka jarak titik P ke garis TQ sama dengan PQ =
Gimana, penjelasannya mudah dimengerti ‘kan? Mau latihan soal lebih banyak lagi? Buka aja aplikasi Ruangguru karena banyak latihan soal matematika IPS kelas 12 yang bisa kamu kerjakan di ruangbelajar.
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<h1 class="content-title">
Latihan Soal Penilaian Tengah Semester 2019: Matematika IPS Kelas XII </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/shabrina-alfari" class="">Shabrina Alfari</a> </p>
<p class="content-info"><span>September 18, 2019 • </span> <span>4 minutes read</span></p>
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<p style="text-align: justify;"><em><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/UN_-_Latihan_Soal_Penilaian_Tengah_Semester_Matematika_Soshum_kelas_12-01.png" alt="latihan soal matematika ips kelas 12" width="820" /></em></p>
<p><span id="more-7792"></span></p>
<p style="text-align: justify;"><em>Artikel ini memberikan latihan soal beserta pembahasan Penilaian Tengah Semester 2019 matematika IPS kelas 12</em></p>
<p style="text-align: center;">—</p>
<p style="text-align: justify;">Apa <em>sih</em> mata pelajaran yang menurut kamu paling sulit? Pasti salah satunya adalah matematika <em>‘kan</em>? Untuk menguasai seluruh materi matematika di Penilaian Tengah Semester, kamu tentu membutuhkan banyak latihan. <em>Nah</em> tunggu apalagi, ayo langsung saja simak latihan soal beserta pembahasan Penilaian Tengah Semester matematika IPS kelas 12 berikut ini.</p>
<h3 style="text-align: justify;"><strong><span style="color: #990100;">Baca juga:</span> <a href="/latihan-soal-ujian-nasional-sma-2019-matematika-ips-dan-pembahasannya" rel=" noopener">Latihan Soal Ujian Nasional SMA 2019 Matematika IPS dan Pembahasannya</a></strong></h3>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik:</strong> <strong>Bidang Datar</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Prinsip Kesebangunan</strong></p>
<ol style="text-align: justify;">
<li>Perhatikan gambar bangun datar di bawah ini!</li>
</ol>
<p style="text-align: justify;"><img decoding="async" style="width: 276px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1-405577069095.png" alt="1-405577069095" width="276" /></p>
<p style="text-align: justify;">Jika garis DE sejajar garis FG sejajar garis BC maka nilai <img decoding="async" style="width: 67px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2-93.png" alt="2-93" width="67" /></p>
<p><img decoding="async" style="width: 53px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/3-56.png" alt="3-56" width="53" /></p>
<p style="text-align: justify;"><strong>Jawaban:</strong> <strong>C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Perhatikan segitiga ADE sebangun dengan segitiga AFG sehingga diperoleh persamaan:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 83px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/4-26.png" alt="4-26" width="83" /></p>
<p style="text-align: justify;">Kemudian perhatikan segitiga ADE sebangun dengan segitiga ABC sehingga diperoleh persamaan :</p>
<p style="text-align: justify;"><img decoding="async" style="width: 95px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5-27.png" alt="5-27" width="95" /></p>
<p style="text-align: justify;">Jadi nilai <img decoding="async" style="width: 128px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/6-24.png" alt="6-24" width="128" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik:</strong> <strong>Bidang Datar</strong></p>
<p style="text-align: justify;"><strong>Subtopik:</strong> <strong>Dalil Dua Garis</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">2. Perhatikan gambar di bawah ini!</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 226px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/7-23.png" alt="7-23" width="226" /></p>
<p style="text-align: justify;">Jika garis DE sejajar dengan garis BC dan panjang AD = 4 cm, BD = 6 cm, AE = x cm dan EC = 9 cm maka nilai dari <img decoding="async" style="width: 41px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8-23.png" alt="8-23" width="41" /></p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>8</li>
<li>9</li>
<li>10</li>
<li>12</li>
<li>18</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban:</strong> D</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Gunakan dalil intersep untuk gambar pada soal.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 80px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/9-27.png" alt="9-27" width="80" /></p>
<p style="text-align: justify;">Maka nilai dari <img decoding="async" style="width: 103px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/10-21.png" alt="10-21" width="103" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik:</strong> <strong>Bidang Datar</strong></p>
<p style="text-align: justify;"><strong>Subtopik:</strong> <strong>Dalil Menelaus & Dalil Ceva</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">3. Perhatikan gambar di bawah ini!</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 273px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/11-130.png" alt="11-130" width="273" /></p>
<p style="text-align: justify;">Nilai <img decoding="async" style="width: 18px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/12-20.png" alt="12-20" width="18" /> yang tepat untuk gambar di atas adalah ….</p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>2,5</li>
<li>3,0</li>
<li>3,5</li>
<li>4,0</li>
<li>4,5</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban:</strong> D</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Gunakan dalil Menelaus untuk gambar pada soal.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 110px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/13-18.png" alt="13-18" width="110" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik:</strong> <strong>Bidang Datar</strong></p>
<p style="text-align: justify;"><strong>Subtopik:</strong> <strong>Garis Istimewa Segitiga I</strong></p>
<p style="text-align: justify;">4. Perhatikan gambar berikut ini!</p>
<p style="text-align: justify;"><img decoding="async" style="width: 293px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/14-5577069082.png" alt="14-5577069082" width="293" /></p>
<p style="text-align: justify;">Jika luas segitiga ACD dan BCD berturut-turut adalah <img decoding="async" style="width: 47px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/15-15.png" alt="15-15" width="47" /> dan <img decoding="async" style="width: 46px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/16-14.png" alt="16-14" width="46" /> maka panjang BD adalah ….</p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>4,0</li>
<li>4,5</li>
<li>5,0</li>
<li>5,5</li>
<li>6,0</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban:</strong> D</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Perhatikan bahwa:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 88px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/17-12.png" alt="17-12" width="88" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik:</strong> <strong>Bidang Ruang: Kedudukan dan Proyeksi</strong></p>
<p style="text-align: justify;"><strong>Subtopik:</strong> <strong>Ulasan Bangun Ruang</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">5. Perhatikan bangun ruang di bawah ini.</span></p>
<p style="text-align: justify;"><span style="background-color: transparent;"><img decoding="async" style="width: 458px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/18-12.png" alt="18-12" width="458" /></span></p>
<p style="text-align: justify;">Bangun ruang yang tidak memiliki diagonal ruang adalah ….</p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>(i) dan (ii)</li>
<li>(ii) dan (iii)</li>
<li>(i) dan (iii)</li>
<li>(ii) dan (iv)</li>
<li>(i) dan (iv)</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban:</strong> E</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Ingat bahwa diagonal ruang adalah ruas garis yang menghubungkan dua titik sudut yang berhadapan dalam suatu bangun ruang.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 498px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/19-11.png" alt="19-11" width="498" /></p>
<p style="text-align: justify;">Pada gambar (i) dan (iv) hanya terdapat diagonal sisi saja (garis biru).</p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik:</strong> <strong>Bidang Ruang: Kedudukan dan Proyeksi</strong></p>
<p style="text-align: justify;"><strong>Subtopik:</strong> <strong>Kedudukan Garis terhadap Garis</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">6. Garis yang sejajar dengan garis AH adalah….</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 196px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/20-10.png" alt="20-10" width="196" /></p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>CF</li>
<li>EF</li>
<li>EC</li>
<li>DC</li>
<li>CH</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban:</strong> A</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Garis AH berada pada bidang ADHE, sedangkan bidang yang sejajar dengan ADHE adalah bidang BCGF, maka garis yang sejajar dengan bidang AH adalah garis yang berada pada bidang BCGF. Jadi garis AH sejajar dengan CF.</p>
<p style="text-align: justify;">Garis AH bersilangan dengan garis EF, EC dan DC.</p>
<p style="text-align: justify;">Garis AH berpotongan dengan CH di titik H.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik: Bidang Ruang: Kedudukan dan Proyeksi</strong></p>
<p style="text-align: justify;"><strong>Subtopik: Kedudukan Bidang terhadap Bidang</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">7. Perhatikan kubus di bawah ini.</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 196px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/20-10.png" alt="20-10" width="196" /></p>
<p style="text-align: justify;">Bidang AFH dan bidang BDG adalah bidang yang saling ….</p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>Sejajar karena memiliki satu garis persekutuan</li>
<li>Sejajar karena tidak memiliki garis persekutuan</li>
<li>Berpotongan karena memiliki titik potong</li>
<li>Berpotongan karena memiliki garis potong</li>
<li>Bersilangan karena tidak saling bertemu</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban:</strong> B</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Perhatikan gambar kedua bidang tersebut.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 198px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/21-9.png" alt="21-9" width="198" /></p>
<p style="text-align: justify;">Dari gambar di atas maka kedua bidang saling sejajar karena tidak memiliki garis persekutuan.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik:</strong> <strong>Bidang Ruang: Jarak</strong></p>
<p style="text-align: justify;"><strong>Subtopik:</strong> <strong>Jarak Titik ke Titik</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">8. Diketahui sebuah kubus ABCD.EFGH dengan rusuk 8 cm seperti pada gambar di bawah ini.</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 196px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/20-10.png" alt="20-10" width="196" /></p>
<p style="text-align: justify;">Jika titik P terletak pada garis AG dengan AP : AG = 1 : 4, maka jarak titik B ke titik P adalah ….</p>
<p><img decoding="async" style="width: 91px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/22-10.png" alt="22-10" width="91" /></p>
<p style="text-align: justify;"><strong>Jawaban:</strong> A</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Perhatikan gambar kubus di bawah ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 222px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/23-7.png" alt="23-7" width="222" /></p>
<p style="text-align: justify;">Diketahui rusuk = 8 cm maka,</p>
<p style="text-align: justify;"><img decoding="async" style="width: 256px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/24-6.png" alt="24-6" width="256" /></p>
<p style="text-align: justify;">Dari segitiga siku-siku ABG diperoleh :</p>
<p style="text-align: justify;"><img decoding="async" style="width: 165px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/25-6.png" alt="25-6" width="165" /></p>
<p style="text-align: justify;">Sedangkan dengan menggunakan aturan cos pada segitiga APB maka diperoleh :</p>
<p style="text-align: justify;"><img decoding="async" style="width: 282px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/26-5.png" alt="26-5" width="282" /></p>
<p style="text-align: justify;">Jadi jarak titik B ke titik P adalah <img decoding="async" style="width: 64px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/27-5.png" alt="27-5" width="64" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik:</strong> <strong>Bidang Ruang: Jarak</strong></p>
<p style="text-align: justify;"><strong>Subtopik:</strong> <strong>Jarak Titik ke Garis</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">9. Diketahui kubus ABCD.EFGH dengan rusuk 5 cm seperti gambar di bawah ini. Jarak titik E ke rusuk BC adalah ….</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 196px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/20-10.png" alt="20-10" width="196" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 81px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/28-5.png" alt="28-5" width="81" /></p>
<p style="text-align: justify;"><strong>Jawaban:</strong> A</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Perhatikan segitiga EBC pada kubus di bawah ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 202px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/29-4.png" alt="29-4" width="202" /></p>
<p style="text-align: justify;">Karena segitiga EBC adalah segitiga siku-siku di B maka jarak terdekat titik E ke garis BC adalah EB <img decoding="async" style="width: 146px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/30-3.png" alt="30-3" width="146" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
<p style="text-align: justify;"><strong>Topik:</strong> <strong>Bidang Ruang: Jarak</strong></p>
<p style="text-align: justify;"><strong>Subtopik:</strong> <strong>Jarak Dua Garis Bersilangan</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent;">10. Diketahui limas T.ABCD dengan alas berbentuk persegi. Rusuk tegak 10 cm dan rusuk alas 8 cm. Jika titik M adalah titik tengah rusuk AD maka jarak garis TM ke garis AB adalah …. Cm</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 289px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/31-3.png" alt="31-3" width="289" /></p>
<ol style="list-style-type: upper-alpha; text-align: justify;">
<li>2</li>
<li>3</li>
<li>4</li>
<li>5</li>
<li>6</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban:</strong> C</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Perhatikan gambar di bawah ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 230px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/32-2.png" alt="32-2" width="230" /></p>
<p style="text-align: justify;">Jika kita buat bidang yang sejajar garis AB dan memuat garis TM yaitu bidang TMN seperti gambar di bawah ini maka jarak</p>
<p style="text-align: justify;"><img decoding="async" style="width: 226px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/33-5.png" alt="33-5" width="226" /></p>
<p style="text-align: justify;">Maka jaraknya berubah jadi jarak garis sejajar bidang.</p>
<p style="text-align: justify;">Misalkan titik P dan Q berturut-turut adalah titik tengah rusuk AB dan garis MN, kemudian proyeksikan titik P ke garis TQ seperti pada gambar di bawah ini.</p>
<p style="text-align: justify;"><img decoding="async" style="width: 231px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/34-2.png" alt="34-2" width="231" /></p>
<p style="text-align: justify;">Karena TPQ adalah segitiga siku-siku di Q maka jarak titik P ke garis TQ sama dengan PQ = <img decoding="async" style="width: 117px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/35-2.png" alt="35-2" width="117" /></p>
<p style="text-align: justify;"><img decoding="async" style="width: 820px;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Untitled%20design%20(2)-30.png" alt="Untitled design (2)-30" width="820" /></p>
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<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Ruangguru</p>
<ul type="none">
<li><a href="https://roboguru.ruangguru.com" target="_blank">Roboguru</a></li>
<li><a href="https://www.ruangguru.com/roboguruplus">Roboguru Plus</a></li>
<li><a href="https://www.ruangguru.com/dafa-lulu">Dafa dan Lulu</a></li>
<li><a href="https://www.ruangguru.com/for-kids/kursus">Kursus for Kids</a></li>
<li><a href="https://www.ruangguru.com/for-kids">Ruangguru for Kids</a></li>
<li><a href="https://www.ruangguru.com/bisnis">Ruangguru for Business</a></li>
<li><a href="https://www.ruangguru.com/ruanguji">Ruanguji</a></li>
<li><a href="https://www.ruangguru.com/blog">Ruangbaca</a></li>
<li><a href="https://www.ruangguru.com/ruangkelas">Ruangkelas</a></li>
<li><a href="https://www.ruangguru.com/ruangbelajar">Ruangbelajar</a></li>
<li><a href="https://pengajar.ruangguru.com/">Ruangpengajar</a></li>
<li><a href="https://www.ruangguru.com/privat">Ruangguru Privat</a></li>
<li><a href="https://www.ruangpeduli.org/" target="_blank">Ruangpeduli</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Bantuan & Panduan</p>
<ul type="none">
<li><a href="https://www.ruangguru.com/company-credentials">Company Credentials</a></li>
<li><a href="https://www.ruangguru.com/beasiswa">Beasiswa Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
<li><a href="https://www.english-academy.id/" target="_blank">English Academy</a></li>
<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>